Problem: Solve for $b$. $\dfrac23b + 5 = 20 - b$ $b =$
Answer: We need to manipulate the equation to get $b$ by itself. $\begin{aligned} \dfrac23b + 5 &= 20 - b \\\\ \dfrac23b + 5 {+b} &= 20 - b {+ b} &&\gray{\text{Add b to each side.}}\\\\ \dfrac53b+5 &= 20 &&\gray{\text{Combine like terms.}}\\\\ \dfrac53b+5 {-5} &= 20 {- 5} &&\gray{\text{Subtract 5 from each side.}}\\\\ \dfrac53b &= 15 &&\gray{\text{Combine like terms.}}\\\\ \dfrac53b\cdot {\dfrac35}&= 15 \cdot {\dfrac35}&&\gray{\text{Multiply each side by}\dfrac35.} \\\\ b &= {9} &&\gray{\text{Simplify.}}\\\\ \end{aligned}$ The answer: $b = {9}~~~~~~~~$ [Let's check our work!]